Simplifying an expression with radicals

Question

So my sister got this task for her homework.

$$\sqrt{18}-\frac{\sqrt{50}}{3\sqrt{3}}=$$

From previos equation she needs to get this:

$$3\sqrt{2}-\frac{5\sqrt{6}}{9}$$

Now I tried to get that but I'm constantly getting:

$$3\sqrt{2}-\frac{5\sqrt{2}}{3\sqrt{3}}$$

Is there anyone who can show, step by step how to get the mentioned result. Thanks a lot :)

Answer 1

This is a matter of getting rid of square roots in the denominator:

$$\frac{1}{\sqrt{X}} = \frac{\sqrt{X}}{\sqrt{X}\sqrt{X}} = \frac{\sqrt{X}}{X}$$

Answer 2

Your first simplification is not correct. $\sqrt {18}=3 \sqrt 2$, but $\sqrt {50}=5 \sqrt 2$. You are then dividing out $\sqrt 3$ in the second step, but it should not be there from the first.